New analysis and application of fractional order Schrödinger equation using with Atangana–Batogna numerical scheme

In this work, an analytical approximation to the solution of Schrodinger equation has been provided. The fractional derivative used in this equation is the Caputo derivative. The existence and uniqueness conditions of solutions for the proposed model are derived based on the power law. While solving...

Full description

Saved in:
Bibliographic Details
Published in:Numerical methods for partial differential equations 2021-01, Vol.37 (1), p.196-209
Main Authors: Akçetin, Eyüp, Koca, Ilknur, Kiliç, Muhammet Burak
Format: Article
Language:English
Subjects:
fractional order differentiation
Mathematical models
Nonlinear equations
Numerical methods
numerical scheme
Schrodinger equation
Schrödinger equation
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c2975-6160ef7fd1776ac392a15e8e977768d6d56630d79d4ee48987a5b1531c9d0e363
cites cdi_FETCH-LOGICAL-c2975-6160ef7fd1776ac392a15e8e977768d6d56630d79d4ee48987a5b1531c9d0e363
container_end_page 209
container_issue 1
container_start_page 196
container_title Numerical methods for partial differential equations
container_volume 37
creator Akçetin, Eyüp
Koca, Ilknur
Kiliç, Muhammet Burak
description In this work, an analytical approximation to the solution of Schrodinger equation has been provided. The fractional derivative used in this equation is the Caputo derivative. The existence and uniqueness conditions of solutions for the proposed model are derived based on the power law. While solving the fractional order Schrodinger equation, Atangana–Batogna numerical method is presented for fractional order equation. We obtain an efficient recurrence relation for solving these kinds of equations. To illustrate the usefulness of the numerical scheme, the numerical simulations are presented. The results show that the numerical scheme is very effective and simple.
doi_str_mv 10.1002/num.22525
format article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2463117316</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2463117316</sourcerecordid><originalsourceid>FETCH-LOGICAL-c2975-6160ef7fd1776ac392a15e8e977768d6d56630d79d4ee48987a5b1531c9d0e363</originalsourceid><addsrcrecordid>eNp1kE1OwzAQhS0EEqWw4AaWWLFIazuxHS9LxZ9UYAGV2FkmnrSp0iS1E1XdcQfuwgW4CSfBJWxZzbzRN09vBqFzSkaUEDauuvWIMc74ARpQotKIJUwcogGRiYooV6_H6MT7FSGUcqoGqHuELTaVKXe-8KGx2DRNWWSmLeoK1znOncn2vSlx7Sw4_Jwt3denLapFELDperLzYYC3RbvEk9ZUi2D5_f5xZdp6URkcUoELpiX22RLWcIqOclN6OPurQzS_uX6Z3kWzp9v76WQWZUxJHgkqCOQyt1RKYbJYMUM5pKBk0KkVlgsREyuVTQCSVKXS8DfKY5opSyAW8RBd9L6Nqzcd-Fav6s6FW7xmiYgplTHdU5c9lbnaewe5blyxNm6nKdH7r-qQX_9-NbDjnt0WJez-B_Xj_KHf-AFLWHwX</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2463117316</pqid></control><display><type>article</type><title>New analysis and application of fractional order Schrödinger equation using with Atangana–Batogna numerical scheme</title><source>Wiley-Blackwell Read &amp; Publish Collection</source><creator>Akçetin, Eyüp ; Koca, Ilknur ; Kiliç, Muhammet Burak</creator><creatorcontrib>Akçetin, Eyüp ; Koca, Ilknur ; Kiliç, Muhammet Burak</creatorcontrib><description>In this work, an analytical approximation to the solution of Schrodinger equation has been provided. The fractional derivative used in this equation is the Caputo derivative. The existence and uniqueness conditions of solutions for the proposed model are derived based on the power law. While solving the fractional order Schrodinger equation, Atangana–Batogna numerical method is presented for fractional order equation. We obtain an efficient recurrence relation for solving these kinds of equations. To illustrate the usefulness of the numerical scheme, the numerical simulations are presented. The results show that the numerical scheme is very effective and simple.</description><identifier>ISSN: 0749-159X</identifier><identifier>EISSN: 1098-2426</identifier><identifier>DOI: 10.1002/num.22525</identifier><language>eng</language><publisher>Hoboken, USA: John Wiley &amp; Sons, Inc</publisher><subject>fractional order differentiation ; Mathematical models ; Nonlinear equations ; Numerical methods ; numerical scheme ; Schrodinger equation ; Schrödinger equation</subject><ispartof>Numerical methods for partial differential equations, 2021-01, Vol.37 (1), p.196-209</ispartof><rights>2020 Wiley Periodicals LLC</rights><rights>2021 Wiley Periodicals LLC.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c2975-6160ef7fd1776ac392a15e8e977768d6d56630d79d4ee48987a5b1531c9d0e363</citedby><cites>FETCH-LOGICAL-c2975-6160ef7fd1776ac392a15e8e977768d6d56630d79d4ee48987a5b1531c9d0e363</cites><orcidid>0000-0002-9608-5250</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27923,27924</link.rule.ids></links><search><creatorcontrib>Akçetin, Eyüp</creatorcontrib><creatorcontrib>Koca, Ilknur</creatorcontrib><creatorcontrib>Kiliç, Muhammet Burak</creatorcontrib><title>New analysis and application of fractional order Schrödinger equation using with Atangana–Batogna numerical scheme</title><title>Numerical methods for partial differential equations</title><description>In this work, an analytical approximation to the solution of Schrodinger equation has been provided. The fractional derivative used in this equation is the Caputo derivative. The existence and uniqueness conditions of solutions for the proposed model are derived based on the power law. While solving the fractional order Schrodinger equation, Atangana–Batogna numerical method is presented for fractional order equation. We obtain an efficient recurrence relation for solving these kinds of equations. To illustrate the usefulness of the numerical scheme, the numerical simulations are presented. The results show that the numerical scheme is very effective and simple.</description><subject>fractional order differentiation</subject><subject>Mathematical models</subject><subject>Nonlinear equations</subject><subject>Numerical methods</subject><subject>numerical scheme</subject><subject>Schrodinger equation</subject><subject>Schrödinger equation</subject><issn>0749-159X</issn><issn>1098-2426</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp1kE1OwzAQhS0EEqWw4AaWWLFIazuxHS9LxZ9UYAGV2FkmnrSp0iS1E1XdcQfuwgW4CSfBJWxZzbzRN09vBqFzSkaUEDauuvWIMc74ARpQotKIJUwcogGRiYooV6_H6MT7FSGUcqoGqHuELTaVKXe-8KGx2DRNWWSmLeoK1znOncn2vSlx7Sw4_Jwt3denLapFELDperLzYYC3RbvEk9ZUi2D5_f5xZdp6URkcUoELpiX22RLWcIqOclN6OPurQzS_uX6Z3kWzp9v76WQWZUxJHgkqCOQyt1RKYbJYMUM5pKBk0KkVlgsREyuVTQCSVKXS8DfKY5opSyAW8RBd9L6Nqzcd-Fav6s6FW7xmiYgplTHdU5c9lbnaewe5blyxNm6nKdH7r-qQX_9-NbDjnt0WJez-B_Xj_KHf-AFLWHwX</recordid><startdate>202101</startdate><enddate>202101</enddate><creator>Akçetin, Eyüp</creator><creator>Koca, Ilknur</creator><creator>Kiliç, Muhammet Burak</creator><general>John Wiley &amp; Sons, Inc</general><general>Wiley Subscription Services, Inc</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>H8D</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0002-9608-5250</orcidid></search><sort><creationdate>202101</creationdate><title>New analysis and application of fractional order Schrödinger equation using with Atangana–Batogna numerical scheme</title><author>Akçetin, Eyüp ; Koca, Ilknur ; Kiliç, Muhammet Burak</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2975-6160ef7fd1776ac392a15e8e977768d6d56630d79d4ee48987a5b1531c9d0e363</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>fractional order differentiation</topic><topic>Mathematical models</topic><topic>Nonlinear equations</topic><topic>Numerical methods</topic><topic>numerical scheme</topic><topic>Schrodinger equation</topic><topic>Schrödinger equation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Akçetin, Eyüp</creatorcontrib><creatorcontrib>Koca, Ilknur</creatorcontrib><creatorcontrib>Kiliç, Muhammet Burak</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical &amp; Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Aerospace Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts – Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Numerical methods for partial differential equations</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Akçetin, Eyüp</au><au>Koca, Ilknur</au><au>Kiliç, Muhammet Burak</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>New analysis and application of fractional order Schrödinger equation using with Atangana–Batogna numerical scheme</atitle><jtitle>Numerical methods for partial differential equations</jtitle><date>2021-01</date><risdate>2021</risdate><volume>37</volume><issue>1</issue><spage>196</spage><epage>209</epage><pages>196-209</pages><issn>0749-159X</issn><eissn>1098-2426</eissn><abstract>In this work, an analytical approximation to the solution of Schrodinger equation has been provided. The fractional derivative used in this equation is the Caputo derivative. The existence and uniqueness conditions of solutions for the proposed model are derived based on the power law. While solving the fractional order Schrodinger equation, Atangana–Batogna numerical method is presented for fractional order equation. We obtain an efficient recurrence relation for solving these kinds of equations. To illustrate the usefulness of the numerical scheme, the numerical simulations are presented. The results show that the numerical scheme is very effective and simple.</abstract><cop>Hoboken, USA</cop><pub>John Wiley &amp; Sons, Inc</pub><doi>10.1002/num.22525</doi><tpages>27</tpages><orcidid>https://orcid.org/0000-0002-9608-5250</orcidid></addata></record>
fulltext fulltext
identifier ISSN: 0749-159X
ispartof Numerical methods for partial differential equations, 2021-01, Vol.37 (1), p.196-209
issn 0749-159X
1098-2426
language eng
recordid cdi_proquest_journals_2463117316
source Wiley-Blackwell Read & Publish Collection
subjects fractional order differentiation
Mathematical models
Nonlinear equations
Numerical methods
numerical scheme
Schrodinger equation
Schrödinger equation
title New analysis and application of fractional order Schrödinger equation using with Atangana–Batogna numerical scheme
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-09T07%3A56%3A28IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=New%20analysis%20and%20application%20of%20fractional%20order%20Schr%C3%B6dinger%20equation%20using%20with%20Atangana%E2%80%93Batogna%20numerical%20scheme&rft.jtitle=Numerical%20methods%20for%20partial%20differential%20equations&rft.au=Ak%C3%A7etin,%20Ey%C3%BCp&rft.date=2021-01&rft.volume=37&rft.issue=1&rft.spage=196&rft.epage=209&rft.pages=196-209&rft.issn=0749-159X&rft.eissn=1098-2426&rft_id=info:doi/10.1002/num.22525&rft_dat=%3Cproquest_cross%3E2463117316%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c2975-6160ef7fd1776ac392a15e8e977768d6d56630d79d4ee48987a5b1531c9d0e363%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2463117316&rft_id=info:pmid/&rfr_iscdi=true